[Puzzler] A Pair of Aces

[Mike]

This is to follow up , because they work out the same muscles:

You have four cards: Ace of Spades, Ace of Hearts, 2 of Spades, 2 of Hearts.

The four cards are shuffled, and you draw two cards at random.

Two scenarios:

1) What is the chance that you drew a pair of Aces if you know that at least one card is an Ace?

2) What is the chance that you drew a pair of Aces if you know that one card is the Ace of Spades?

[Zen]

I'm not sure, but I can tell you that the chances of you having a pair of aces if you don't have at least one ace is 0%.

Okay, more seriously...

If you know one card is an Ace:



If you know 1 card is the Ace of Spades.

[Mike]

Zen wins all the candy!

[Zen]

Well, I should be able to do this stuff... I used to use versions of combinations and permutations for my grad school research on the effects of superficial similarity of novice problem solving... Not that I had to do the problems, but I looked at them a lot... a WHOLE lot!

[Phoebe]

Ok if you know it's the ace of spades

[Eliahad]

Phoebe, it has to do with counting the number of possible cases, and not just the cards left in the draw pile. If you lay out all the possible outcomes (since this is small enough to do), you will see that there are more possible outcomes than just the next draw.

Your feelings about this puzzle remind me of a different one. The shell game probability puzzle never sat well with me. (The one where the huckster puts a pea under one shell. Mixes them up, and then reveals one of the shells that doesn't hold the pea. The odds of picking the correct shell do NOT increase to 50%, but even after seeing the explanation, it still bugs me.)